title: Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.
abstract: The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.
authors.affiliation: Department of Micro- and Nanotechnology, DTU Nanotech, Technical University of Denmark, Building 345E, DK-2800 Lyngby, Denmark. kasper.reck@nanotech.dtu.dk
authors.forename: Kasper
authors.initials: K
authors.lastname: Reck
authors.forename: Erik V
authors.initials: EV
authors.lastname: Thomsen
authors.forename: Ole
authors.initials: O
authors.lastname: Hansen
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004574:Electromagnetic Fields; D005583:Fourier Analysis; D008962:Models, Theoretical; D012542:Scattering, Radiation